3x^2+21x-5=0

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Solution for 3x^2+21x-5=0 equation:


Simplifying
3x2 + 21x + -5 = 0

Reorder the terms:
-5 + 21x + 3x2 = 0

Solving
-5 + 21x + 3x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-1.666666667 + 7x + x2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + 7x + 1.666666667 + x2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + 7x + x2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + 7x + x2 = 0 + 1.666666667
7x + x2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
7x + x2 = 1.666666667

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 1.666666667 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 1.666666667 + 12.25

Combine like terms: 1.666666667 + 12.25 = 13.916666667
12.25 + 7x + x2 = 13.916666667

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 13.916666667

Calculate the square root of the right side: 3.730504881

Break this problem into two subproblems by setting 
(x + 3.5) equal to 3.730504881 and -3.730504881.

Subproblem 1

x + 3.5 = 3.730504881 Simplifying x + 3.5 = 3.730504881 Reorder the terms: 3.5 + x = 3.730504881 Solving 3.5 + x = 3.730504881 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 3.730504881 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 3.730504881 + -3.5 x = 3.730504881 + -3.5 Combine like terms: 3.730504881 + -3.5 = 0.230504881 x = 0.230504881 Simplifying x = 0.230504881

Subproblem 2

x + 3.5 = -3.730504881 Simplifying x + 3.5 = -3.730504881 Reorder the terms: 3.5 + x = -3.730504881 Solving 3.5 + x = -3.730504881 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -3.730504881 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -3.730504881 + -3.5 x = -3.730504881 + -3.5 Combine like terms: -3.730504881 + -3.5 = -7.230504881 x = -7.230504881 Simplifying x = -7.230504881

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.230504881, -7.230504881}

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